JEE Main Sample Paper B.Tech Set D

JEE MAIN
SAMPLE
PAPER
Paper 1 for B.Tech

SET D
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Jee Main Sample Paper

Physics

Q1. The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In
another 10s it will decrease to α times its original magnitude, where α equals.
1. 0.81
2. 0.729
3. 0.6
4. 0.7

Q2. In an a.c. circuit, the instantaneous e.m.f. and current are given by e=100 sin 30 t, i=20 sin
(30t - π/4) In one cycle of a.c., the average power consumed by the circuit and the wattless current
are, respectively :
1. 50, 10
2. 1000/√2, 10
3. 50/√2 , 0
4. 50 , 0

Q3. For an RLC circuit driven with voltage of amplitude vm and frequency ωo = 1/√LC the current
exibits resonance. The quality factor, Q is given by :
1. ωoL/R
2. ωoR/L
3. R/(ωoC)
4. CR/ωo

Correct. 1

Q4. In the given circuit diagram when the current reaches steady state in the circuit, the charge on
the capacitor of capacitance C will be:

1. CE

2. CE r1/(r2 + r)
3. CE r2 / (r+ r2)
4. CE r1 / (r1 + r)

Q5. Which of the following statements is false ?
1. Wheatstone bridge is the most sensitive when all the four resistances are of the same order of
magnitude.
2. In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point
is disturbed.
3. A rheostat can be used as a potential divider.
4. Kirchhoff’s second law represents energy conservation.

Q6. A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30° from
the horizontal as shown and released from rest. Its angular speed when it passes through the
horizontal ( in rads −1
) will be (g = 10ms −2
)

1. √30/2
2. v30/2
3. √30
4. √20/3

Q7. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat
transferred to the gas, so that rms velocity of molecules is doubled, is about : (Take R=8.3J/K mole)
1. 14 kJ
2. 10 kJ
3. 0.9 kJ
4. 6 kJ

Q8. The The energy associated with electric eld is (U ) and with magnetic eld is (U ) for an
E B

electromagnetic wave in free space. Then:
1. U > U E B

2. U
UB

E =
2

3. U E = UB

4. U E < UB

Q9. In the given circuit the internal resistance In the of the 18 V cell is negligible. If R = 400Ω,
1

R = 100Ω and R = 500Ω and the reading of an ideal voltmeter across R is 5 V, then the value
3 4 4

of R will be:
2

1. 450Ω
2. 550Ω
3. 230Ω
4. 300Ω

Q10. The region between y=0 and y=d contains a magnetic eld B → = Bz. A particle of mass m and
→ = v^i . If d =
charge q enters the region with a velocity v the acceleration of the charged
mv

2qB

particle at the point of its emergence at the other side is :
^
i +^
1.
qvB j
( )
m
√2

qvB −^
j+^
i
2. m
( )
√2

3.
qvB √3 1
( i + i)
m 2 2

qvB √3
4.
1 ^ ^
( i − j)
m 2 2

Q11. Two guns A and B can re bullets at speeds 1 km/s and 2 km/s respectively. From a point on a
horizontal ground, they are red in all possible directions. The ratio of maximum areas covered by
the bullets red by the two guns, on the ground is :

1. 1:2
2. 1:16
3. 1:4
4. 1:8

Q12. Three Carnot engines operate in series between a heat source at a temperature T, and a heat
sink at temperature T4 (see gure). There are two other reservoirs at temperature T, and T3, as
shown, with T2 > T2 > T2 > T4. The three engines are equally ef cient if

1/4 1/4
1. T
3 3
2 = (T T4 ) ; T3 = (T1 T )
1 4

1/3 1/3
2. T
2 2
2 = (T1 T4 ) ; T3 = (T1 T )
4

1/3 1/3
3. T 2 = (T1 T )
2

4
2
; T3 = (T T4 )
1

1/3
4. T
1/2 2
2 = (T1 T4 ) ; T3 = (T1 T4 )

Q13. A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε and
internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length
AJ at which the galvanometer as shown in g. shows no de ection is :

1. 5/12L
2. 11/12L

3. 13/24 L
4. 11.24L

Q14. A string of length 1 m and mass 5 g is xed at both ends. The tension in the string is 8.0 N.
The string is set into vibration using an external vibrator of frequency 100 Hz. The separation
between successive nodes on the string is close to :
1. 33.3 cm
2. 16.6 cm
3. 20.0 cm
4. 10.0 cm

Q15. A parallel plate capacitor is of area 6cm and a separation 3 mm. The gap is lled with three
2

dielectric materials of equal thickness (see gure) with dielectric constants K = 10, K = 12 and
1 2

K = 14 The dielectric constant of a material which when fully inserted in above capacitor, gives
3

same capacitance would be :

1. 12
2. 36
3. 14
4. 4

Correct. 1

Q16. In an electron microscope, the resolution that can be achieved is of the order of the
wavelength of electrons used. To resolve a width of 7.5 x 10-12 m, the minimum electron energy
required is close to :
1. 1 kev
2. 500 keV
3. 25 keV
4. 100 keV

Q17. In the cube of side 'a' shown in the gure, the vector from the central point of the face ABOD
to the central point of the face BEFO will be :

n n
1. 1

2
a( )
k −i

2.
1 ^ ^
a( j − k)
2

3. 1
a(^ ^
i − k)
2

4. 1

2
^ ^
a( j − i )

Q18. When a certain photo-sensistive surface is illuminated with monochromatic light of
frequency v, the stopping potential for the photo current is . When the surface is illuminated by
monochromatic light of frequency v/2, the stopping potential is - The threshold frequency for
photoelectric emission is :
1. v 4

3

2. 2 v
3. 5v

3

4. 3v

2

Q19. To double the covering range of a TV transmission tower, its height should be multiplied by :
1. 1

√2

2. 2
3. 4
4. √2

Q20. In a radioactive decay chain, the initial nucleus is Th. At the end there are 6 α-particles
232

90

and 4 β-particles which are emitted. If the end nucleus is X, A and Z are given by :
A
Z

1. A= 202; Z=80

2. A= 200; Z=81
3. A= 208; Z=80
4. A= 208 ; Z=82

Q21. Mobility of electrons in a semiconductor is de ned as the ratio of their drift velocity to the
applied electric eld. If, for an n-type semiconductor, the density of electrons is 10¹⁹ m⁻³ and their
mobility is 1.6 m² / (V.s) then the resistivity of the semiconductor (since it is an n-type
semiconductor contribution of holes is ignored) is close to:
1. 0.2 Ωm
2. 4 Ωm
3. 2 Ωm
4. 0.4 Ωm

Q22. A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible
mass) of spring constant k. The other end of the spring is xed, as shown in the gure. The block is
initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the
maximum speed of the block is :

1. F

√mk

2.
F

π√mk

3.
πF

√mk

4. 2f

√mk

Correct. 1

Q23. Two coherent sources produce waves of different intensities which interfere. After
interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of
the waves are in the ratio :
1. 16:9
2. 5:3
3. 25:9
4. 4:1

Q24. Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a
220 V voltage source. If the 25 W and 100 W bulbs draw powers P₁ and P₂ respectively,

1. P₁ = 9 W, P₂ = 16 W
2. P₁ = 16 W, P₂ = 4 W
3. P₁ = 4 W, P₂ = 16 W
4. P₁ = 16 W, P₂ = 9 W

Q25. A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is
the modulation index?
1. 0.4
2. 0.5
3. 0.6
4. 0.3

Chemistry

Q1. Arrange the following compounds in order of decreasing acidity:

1. I > II > III > IV
2. III > I > II > IV
3. IV > III > I > II
4. II > IV > I > III

Q2. Synthesis of each molecule of glucose in photosynthesis involves
1. 10 molecules of ATP
2. 8 molecules of ATP

3. 6 molecules of ATP
4. 18 molecules of ATP

Q3. An organic compound A upon reacting with NH3 gives B. On heating B gives C. C in presence
of KOH reacts with Br2 to give CH3CH2NH2. A is
1. CH3CH2CH2COOH

2.
3. CH3CH2COOH
4. CH3COOH

Q4. In which of the following pairs of molecules/ions, both the species are not likely to exist?
1. H2-, He2 2-
2. H22+, He2
3. H2-, He2 2+
4. H2+, He2 2-

Q5. The compound that does not produce nitrogen gas by the thermal decomposition is :
1. Ba(N₃)₂
2. (NH₄)₂Cr₂O₇
3. NH₄NO₂
4. (NH₄)₂SO₄

Q6. The major product formed in the following reaction is :

1.

2.

3.

4.

Q7.
1. −74.8 kJ mol−1
2. −144.0 kJ mol−1
3. 74.8 KJ mol-1
4. 144.0 KJ mol-1

Correct. 1

Q8. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’,
the closest approach between two atoms in metallic crystal will be :
1. √ 2 a
2. a/√ 2
3. 2a
4. 2√ 2a

Q9. Which of the following molecules is least resonance stabilized ?

1.

2.

3.

4.

Q10. Which of the following compounds will behave as a reducing sugar in an aqueous KOH
solution ?

1.

2.

3.

4.

Q11. The pH of rain water , is approximately :
1. 7.5
2. 6.5
3. 7.0
4. 5.6

Q12. The coordination number of Th in K [Th (C O ) (OH ) ] is : (C O
2−
4 2 4 2 2 = Oxalato )
4 2 4

1. 8
2. 6
3. 14
4. 10

Q13. Given the equilibrium constant : Kc of the reaction:
(aq) + 2Ag(s)is 10x10¹⁵, calculate the E of this reaction at 298 K
+ 2+ θ
Cu(s) + 2Ag (aq) → Cu
cell

RT
[2.303 at 298K = 0.059V]
F

1. 0.04736 V
2. 0.04736 mV
3. 0.4736 mV
4. 0.4736 V

Q14. The reaction that does NOT de ne calcination is:
Δ
1. Fe O
2 3 ⋅ XH2 O ⟶ Fe2 O3 + XH2 O
Δ
2. 2Cu S + 3O
2 2 ⟶ 2Cu2 O + 2SO2
Δ
3. ZnCO 3 ⟶ ZnO + CO2
Δ→

4. CaCO 3 ⋅ MgCO 3
MgO + 2CO2

Q15. Which premitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles
different from 90° ?
1. Monoclinic
2. Hexagonal
3. Triclinic
4. Tetragonal

Q16. The major product formed in the reaction given below will be:

1.

2.

3.

4.

Q17. Wilkinson catalyst is :
1. [(Et P ) Ir C]
3 3

2. [(Et P) RhCl]
3 3

3. [(Ph P) RhCl]
3 3
(Et = C2 H5 )

4. [(Ph P) IrCl]
3 3

Q18. The electronegativity of aluminium is similar to :
1. Lithium
2. Carbon
3. Beryllium
4. Boron

Q19. The major product of the following reaction is :

1. CH₃CH=C=CH₂
2. CH₃CH₂C=CH

3.
4. CH₃CH=CHCH₂NH₂

Q20. The combination of plots which does not represent isothermal expansion of an ideal gas is :

( A)

( B)

( C)

( D)
1. ( B) and ( D)
2. ( A) and ( D)
3. ( B) and ( C)
4. ( A) and ( C)

Correct. 1

Q21. Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3
oxidation states. This is due to:
1. lattice effect
2. lanthanoid contraction
3. inert pair effect
4. diagonal relationship

Q22. The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The
amount of PbSO₄ electrolyzed in g during the process is : (Molar mass of
PbSO₄ =303 g mol⁻¹)
1. 15.2
2. 11.4

3. 7.6
4. 22.8

Q23. Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass
of the gas adsorbed on mass m of the adsorbent at pressure p. x/m is proportional to:

1. p 1/2

2. p 2

3. p 1/4

4. p

Correct. 1

Q24. A metal on combustion in excess air forms X. X upon hydrolysis with water yields H₂O₂, and
O₂ along with another product the metal is :
1. Li
2. Rb
3. Mg
4. Na

Q25. Water samples with BOD values of 4 ppm and 18 ppm, respectively, are:
1. Clean and Highly polluted
2. Highly polluted and Highly polluted
3. Highly polluted and Clean
4. Clean and Clean

Correct. 1

Maths

Q1. If the system of linear equations
x+ky+3z=0
3x+ky−2z=0
2x+4y−3z=0

has a non-zero solution (x, y, z), then xz/y² is equal to :
1. -10
2. 10
3. -30
4. 30

Q2. The integral

1.

2.

3.

4.

Q3.
1. z
2. -1
3. 1
4. -z

Q4. Let k be an integer such that the triangle with vertices (k, −3k), (5, k) and (−k, 2) has area 28 sq.
units. Then the orthocentre of this triangle is at the point :
1. (1,3/4)
2. (1,-3/4)
3. (2,1/2)
4. (2,-1/2)

Q5. The perpendicular distance from the origin to the plane containing the two lines,

y−2 y−4
and , is:
x+2 z+5 x−1 z+4
= = = =
3 5 7 1 4 7

1. 11
2. 6√11
3. 11/√6
4. 11√6

Q6. Let S={1, 2, 3, ... , 100). The number of non-empty subsets A of S such that the product of
elements in A is even is :
1. 2⁵º (2⁵º – 1)
2. 2⁵º – 1
3. 2⁵º + 1
4. 2¹ºº – 1

Correct. 1

cos θ − sin θ
Q7. If A = [ ] then the matrix A⁻⁵º when θ = π

12
, is equal to :
sin θ cos θ

√3 1
⎡ − ⎤
1. ⎢
2 2
⎥
1 √3
⎣ ⎦
2 2

√3 1
⎡ ⎤
2. ⎢ 2 2
⎥
√3
⎣−1 ⎦
2 2

√3 1
⎡ ⎤
3. ⎢
2 2
⎥
√3
⎣−1 ⎦
2 2

1 √3
⎡
4. ⎢ 2 2

√3 1
⎣ −
2 2

Q8. Let α and ß be two roots of the equation x²+2x+2=0, then α¹⁵ + ß¹⁵ is equal to :

1. - 512
2. - 256
3. 256
4. 512

Q9. Let A = { θ ∊ (− is purely imaginary } .Then the sum of the elements in A is:
π 3+2i sin θ
, π) :
2 1−2i sin θ

1. 3π/4
2. 2π/3
3. π
4. 5π/6

2x x
Q10. The integral ∫ is equal to :
e x e
{( ) − ( ) } log xdx
1 e x e

1. 1

2
− e −
1

e2

2. − 1

2
+
1

e
−
2e
1
2

3. 3

2
− e −
1
2
2e

4. 3

2
−
1

e
−
1
2
2e

Q11. There are m men and two women participating in a chess tournament. Each participant plays
two games with every other participant. If the number of games played by the men between
themselves exceeds the number of games played between the men and the women by 84, then the
value of m is :
1. 11
2. 9
3. 12
4. 7

Q12. In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and
NSS. If one of these students is selected at random, then the probability that the student selected
has opted neither for NCC nor for NSS is :

1. 1

6

2. 5

6

3. 1

3

4. 2

3

Correct. 1

Q13. Let n ≥ 2 be a natural number and 0 < 0 < π/2.
n
4
(sin θ−sin θ) cos θ

Then, ∫ n+1
dθ is equal to:
sin θ

(where C is a constant of integration)
n+1

1.
n
n 1
2
(1 − n+1
) + C
n −1 sin θ
n+1

2.
n
n 1
2
(1 − n−1
) + C
n −1 sin θ
n+1

3.
n
n 1
2
(1 + ) + C
n−1
n −1 sin θ
n+1

4.
n
n 1
(1 − ) + C
2 n−1
n +1 sin θ

Q14. Consider the quadratic equation (c − 5)x − 2cx + (c − 4) = 0, c = 5. Let S be the set of
2

all integral values of c for which one root of the equation lies in the interval (0, 2) and its other
root lies in the interval (2,3). Then the number of elements in Sis:
1. 18
2. 12
3. 11
4. 10

^ →
→ = 2^i + λ ^j + 3k, → = 3^i + 6^j + (λ
Q15. Let a b = 4 i + (3 − λ ) j + 6k and c
^
1
^ ^
2 3
^
− 1) k be three
vectors such that → → and a
b = 2a → is perpendicular to c→. Then a possible value of (λ , λ , λ ) is :
1 2 3

1. (− 1

2
, 4, 0)

2. (
1
, 4, −2)
2

3. (1,3,1)
4. (1,5,1)

Correct. 1

Q16. The plane passing through the point (4,-1, 2) and parallel to the lines

x+2 y−2 z+1 x−2 y−3 z−4
= = and = =
3 −1 2 1 2 3

1. (1,1,1)
2. (1,1, -1)
3. (-1, -1,1)
4. (-1,-1, -1)

Correct. 1

Q17. Let f : R → K be a function such that f (x) = x 3 2 ′
+ x f (1) + xf
′′
(2) + f
′′′
(3), x ∈ R .
Then f (2) equals :
1. -4
2. 8
3. 30
4. - 2

Q18. If in a parallelogram ABDC, the coordinates of A, B and Care respectively (1,2), (3, 4) and
(2,5), then the equation of the diagonal AD is
1. 3x+5y-13=0
2. 5x+3y-11=0
3. 5x – 3y+1=0
4. 3r-5y+7=0

Q19. Given for a ΔABC with 13 usual notation. If , then
b+c c+a a+b cos A cos B cos C
= = = =
11 12 13 α β γ

the ordered triad (α, β, ү) has a
1. (3,4,5)
2. (7, 19, 25)
3. (5,12,13)
4. (19,7, 25)

Q20. If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7,0, 6)
and is perpendicular to the plane 2x - 5y=15, then 2α − 3β is equal to :
1. 7

2. 12
3. 17
4. 5

Correct. 1

Q21. If ∫ , where C is a constant of integration, then f(x) is equal
x+1
dx = f (x)√2x − 1 + C
√2x−1

to:
1. (x + 1)
1

3

2. 2

3
(x − 4)

3.
1
(x + 4)
3

4. 2

3
(x + 2)

Q22. For each xeR, let [x] be the greatest integer less than or equal to x. Then
x([x]+|x|) sin[x]
lim
x→0
−
|x|
is equal to :
1. 0
2. 1
3. sin 1
4. -sin 1

Q23. Let the equations of two sides of a triangle be 3x - 2y+6=0 and 4x +5y-20=0. If the orthocentre
of this triangle is at(1, 1), then the equation of its third side is :
1. 26x+61y+1675= 0
2. 122y +26x +1675=0
3. 26x-122y-1675=0
4. 122y-26x - 1675=0

Q24. If both the roots of the quadratic equation x − mx + 4 = 0 are real and distinct and they
2

lie in the interval [1, 5] , then m lies in the interval :
1. (4,5)
2. (5,6)

3. (-5,-4)
4. (3,4)

Correct. 1

Q25. The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1,
3, 7, 9 (repitition of digits allowed) is equal to :
1. 375
2. 374
3. 250
4. 372